Kim "guided the test-fire of (a) new weapon again on Friday morning", the state-run Korean Central News Agency (KCNA) said.
"The national defence scientists showed a perfect result in the test-fire, too, and helped cement bigger confidence in this weapon system.
"It is our party's goal of defence building to possess invincible military capabilities no one dare provoke and to keep bolstering them," KCNA quoted Kim as saying.
"Everyone should remember that it is the party's core plan and fixed will for defence building to possess such a powerful force strong enough to discourage any forces from daring to provoke us."
KCNA did not provide other details on the weapon, including its name, Yonhap News Agency reported.
The report came a day after South Korea's military said that the North fired two projectiles presumed to be short-range ballistic missiles off its east coast. It said that they flew around 230 km at a maximum altitude of 30 km.
Military experts say that the projectiles bear outward similarities to the US' Army Tactical Missile System (ATACMS), a surface-to-surface missile system.
Friday's firing came six days after North Korea flew two projectiles believed to be short-range ballistic missiles, though the North said later it tested a "new weapon". It also was the sixth such launch since late July.
North Korea has carried out weapons tests in recent weeks in apparent protest of the ongoing joint military exercise by South Korea and the US, which it sees as a rehearsal for invasion.
Earlier this week, the North warned that inter-Korean dialogue won't resume unless the South offers a "plausible excuse" for its combined military exercise with the US.
( With inputs from IANS )